Heat oven to 350°F. In a large bowl with an electric mixer on medium, beat butter until creamy. Beat in cream cheese; add sugar and vanilla and beat until combined. On low, beat in flour.
Roll dough into a 16 x 11-inch rectangle between two pieces of waxed paper. Chill in freezer 30 minutes.
Remove top sheet of paper. With long side parallel to you, sprinkle half the dough lengthwise with red sugar crystals and half with green. Using bottom piece of paper to help you, roll up dough in jelly-roll fashion to form a long log. Roll log in white sugar crystals. Wrap in plastic; freeze 30 minutes.
Using a serrated knife, cut log into 5/8-inch slices. Place slices on ungreased baking sheets 1 inch apart. Bake 12 to 14 minutes, until lightly browned and puffy. Cool on sheets 2 minutes. Transfer to wire racks to cool completely.